D6 branes and M theory geometrical transitions from gauged supergravity

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We study the supergravity duals of supersymmetric theories arising in the world-volume of D6 branes wrapping holomorphic two-cycles and special Lagrangian three-cycles within the framework of eight dimensional gauged supergravity. When uplifted to 11d, our solutions represent M-theory on the background of, respectively, the small resolution of the conifold and a manifold with G₂ holonomy. We further discuss on the flop and other possible geometrical transitions and its implications.